One inch is exactly 72 points. The 72 is a modern decision, not a historical inheritance — Adobe chose it for PostScript in the 1980s, and in doing so quietly redefined a unit that had meant something slightly different for a century.
About the units
Before desktop publishing, the point was defined through the pica, and the pica was not exactly a sixth of an inch. The American system standardised in 1886 on a pica of 0.166044 inch, giving 72.27 points to the inch. That value survives in TeX, where the point is still 1/72.27 inch and the PostScript value is called a big point. Adobe rounded to 72 because it made the arithmetic clean for a device-independent imaging model, and the industry followed. The change was under half a per cent and passed almost unremarked outside typesetting circles.
The exact factor
The factor is exactly 72 by modern definition. In metric terms, a point is 25.4 ÷ 72 = 0.352778 mm. The historical values worth knowing when working with old material: the TeX point is 1/72.27 inch, the Didot point is 0.376 mm or about 1/67.5 inch, and the Fournier point was smaller still. A document reset from a nineteenth-century original using modern points will be very slightly tighter than the original, which matters when matching a reprint to an existing edition.
Where you meet this conversion
Font and layout specification across every design discipline. PDF uses points as its native coordinate unit, so page sizes inside the file are expressed in them: US Letter is 612 × 792 points and A4 is 595.28 × 841.89. Those numbers appear in error messages and preflight reports, and recognising them saves diagnosis time. Font metrics — ascent, descent, cap height — are published in units per em that scale against the point size.